First slide

Definition of Work

Question

A uniform force of $(3 \hat{i} + \hat{j})$ newton acts on a particle of mass 2 kg. Hence the particle is displaced from position $(2 \hat{i} + \hat{k})$ meter to position $(4 \hat{i} + 3 \hat{j} - \hat{k})$ meter. The work done by the force on the particle is

Easy

A

13J
B

15J
C

9J
D

6J

Solution

$H e r e, \vec{F} = (3 \hat{i} + \hat{j}) N I n t i t a l p o s i t i o n, {\vec{r}}_{1} = (2 \hat{i} + \hat{k}) m F i n a l p o s i t i o n, {\vec{r}}_{2} = (4 \hat{i} + 3 \hat{j} - \hat{k}) m D i p l a c e m e n t, \vec{r} = (4 \hat{i} + 3 \hat{j} - \hat{k}) m - (2 \hat{i} + \hat{k}) m = 2 \hat{i} + 3 \hat{j} - 2 \hat{k} m W o r k d o n e, W = \vec{F} . \vec{r} = (3 \hat{i} + \hat{j}) . (2 \hat{i} + 3 \hat{j} - 2 \hat{k}) = 6 + 3 = 9 J$

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